Question

How do you know if you can make a right triangle with the square roots line on top of the number like this:

A.2,2, v``4``

B.9,40,41

C.v``5`,10, v``125

What is the methods to find if the numbers can get to a right triangle.

Answer 1

Test for the Pythagorean relationship.
in a right-angled triangle sides a, b, and c, where c is the hypotenuse and obviously the longest side
a^2 + b^2 = c^2

so let's take 2, 2, √4
without even doing anything I can see that it can't be, since √4 = 2 and all sides would be 2
This makes it equilateral, not right-angle

let's look at 9,40,41
clearly 41 is the longest side, so is
9^2 + 40^2 = 41^2
Left side = 81 + 400 = 481
Right sie = 41^2 = 481 , so yes it is right-angled

last one: √5, 10,√125
of those √125 is the longest, so is (√5)^2 + 10^2 = (√125)^2 ?
LS = (√5)^2 + 10^2
= 5 + 100 = 125
RS = (√125)^2 = 125
So yes, it is right-angled